SOLUTION: This question is from a quiz. You must show all relevant steps, list all numbers for which the rational expression is undefined. x^2+6x-27 ___________ x^2+x-6 Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This question is from a quiz. You must show all relevant steps, list all numbers for which the rational expression is undefined. x^2+6x-27 ___________ x^2+x-6 Thank you      Log On


   

Question 155227This question is from textbook elementary and intermediate algebra
: This question is from a quiz. You must show all relevant steps, list all numbers for which the rational expression is undefined.
x^2+6x-27
___________
x^2+x-6
Thank you This question is from textbook elementary and intermediate algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2%2B6x-27%29%2F%28x%5E2%2Bx-6%29 Start with the given expression

x%5E2%2Bx-6=0 Set the denominator equal to zero. Remember, division by zero is not defined.


%28x%2B3%29%28x-2%29=0 Factor the left side


x%2B3=0 or x-2=0 Use the zero product property to set each factor equal to zero


x=-3 or x=2 Solve for "x" in each equation


So if x=-3 or x=2, then the expression x%5E2%2Bx-6 will be zero. Since division by zero is not defined, this means that the values x=-3 and x=2 make the rational expression %28x%5E2%2B6x-27%29%2F%28x%5E2%2Bx-6%29 undefined.